M5120 Linear Models in Statistics I

Faculty of Science
Autumn 2022
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. David Kraus, Ph.D. (lecturer)
Mgr. Jan Holub (seminar tutor)
Mgr. Vojtěch Šindlář (seminar tutor)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 14:00–15:50 M1,01017
  • Timetable of Seminar Groups:
M5120/01: Mon 16:00–17:50 MP1,01014, V. Šindlář
M5120/02: Mon 12:00–13:50 MP1,01014, V. Šindlář
M5120/03: Fri 8:00–9:50 MP1,01014, J. Holub
Prerequisites
M4122 Probability and Statistics II
Calculus, linear algebra. Probability and mathematical statistics, in particular theory of estimation and testing statistical hypotheses: at the level of the course M4122. Statistical software R: at the level of the course M4130.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course offers an overview of linear statistical models as the fundamental tool of statistical analysis. Within one semester, the students encounter theory, software implementation, applications and interpretation.
Learning outcomes
After the course, the students
- are able to recognize the situations that can be addressed by linear models;
- are able to formulate and implement a model, and interpret the results;
- are aware of the limitations of the model;
- in a given situation, they are able to anticipate possible problems and avoid them by slightly modifying the procedure.
Syllabus
  • Problem statement.
  • Descriptive statistics and graphical diagnostics.
  • Projection, conditional expectation, normal distribution.
  • Linear model without the assumption of normality.
  • Linear model with the assumption of normality.
  • Submodel.
  • Residuals and model diagnostics.
  • Multicollinearity and rank-defficient models.
  • Practical aspects, troubleshooting.
Literature
    recommended literature
  • WOOD, Simon N. Generalized additive models : an introduction with R. Boca Raton, Fla.: Chapman & Hall/CRC, 2006, xvii, 392. ISBN 1584884746. info
  • FARAWAY, Julian James. Linear models with R. Boca Raton: Chapman & Hall/CRC, 2005, x, 229. ISBN 1584884258. info
  • ZVÁRA, Karel. Regrese (Regression). Praha, 2008, 253 pp. ISBN 978-80-7378-041-8. info
  • ANDĚL, J. Základy matematické statistiky. Praha: MFF UK, 2005. info
    not specified
  • Applied multivariate statistical analysis. Edited by Richard Arnold Johnson - Dean W. Wichern. 6th ed. Upper Saddle River, N.J.: Pearson Prentice Hall, 2007, xviii, 773. ISBN 9780131877153. info
  • ANDĚL, Jiří. Matematická statistika. Vyd. 2. Praha: SNTL - nakladatelství technické literatury, Alfa, vydavatelstvo technickej a ekonomickej literatury, 1985, 346 s. URL info
  • RAO, C. Radhakrishna. Lineární metody statistické indukce a jejich aplikace. Translated by Josef Machek. Vyd. 1. Praha: Academia, 1978, 666 s. URL info
Teaching methods
Lectures: theoretical explanation with practical examples.
Exercises: exercises focused on in-depth understanding of the theory and on practical data analysis
Assessment methods
Conditions: semestral data project, written final exam, potentially with a bonus for an optional written midterm exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
https://is.muni.cz/auth/el/sci/podzim2022/M5120/index.qwarp
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2022, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2022/M5120